Given the functions, f(x) = 3x2 - 7 and g(x) = x3 + 1, evaluate f(g(2)).

236


To evaluate \( f(g(2)) \), we need to follow these steps:

### Step 1: Find \( g(2) \)
Given the function \( g(x) = x^3 + 1 \), substitute \( x = 2 \):
\[
g(2) = 2^3 + 1 = 8 + 1 = 9
\]

### Step 2: Find \( f(g(2)) = f(9) \)
Now, using the function \( f(x) = 3x^2 - 7 \), substitute \( x = 9 \):
\[
f(9) = 3(9)^2 - 7 = 3(81) - 7 = 243 - 7 = 236
\]

Thus, \( f(g(2)) = 236 \).

Would you like further clarification or more details on any steps? Here are five related questions you might find interesting:

1. What happens if \( g(x) = x^3 - 1 \) instead of \( x^3 + 1 \)?
2. Can you find \( f(g(x)) \) in terms of \( x \) without specific values?
3. What is the derivative of \( f(g(x)) \)?
4. How would you solve \( f(g(x)) = 0 \)?
5. What if we reversed the functions and evaluated \( g(f(2)) \)?

**Tip**: When dealing with composite functions, always evaluate the inner function first before moving on to the outer function.

Given the functions, f(x) = 3x^2 - 7 and g(x) = x^3 + 1, evaluate f(g(2)).

Learn how to evaluate the composite function f(g(2)) with f(x) = 3x^2 - 7 and g(x) = x^3 + 1. This step-by-step solution walks through finding g(2) and then applying it to f(x), covering important algebraic concepts suitable for high school students in Grades 10-12.

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